6=-0.01(x-59)(x-59)+36.81

Solution for 6=-0.01(x-59)(x-59)+36.81 equation:

6=-0.01(x-59)(x-59)+36.81

We move all terms to the left:

6-(-0.01(x-59)(x-59)+36.81)=0

We multiply parentheses ..

-(-0.01(+x^2-59x-59x+3481)+36.81)+6=0


We calculate terms in parentheses: -(-0.01(+x^2-59x-59x+3481)+36.81), so:

-0.01(+x^2-59x-59x+3481)+36.81

We multiply parentheses

-0.01x^2+0.59x+0.59x-34.81+36.81

We add all the numbers together, and all the variables

-0.01x^2+1.18x+2

Back to the equation:

-(-0.01x^2+1.18x+2)


We get rid of parentheses

0.01x^2-1.18x-2+6=0

We add all the numbers together, and all the variables

0.01x^2-1.18x+4=0

a = 0.01; b = -1.18; c = +4;
Δ = b2-4ac
Δ = -1.182-4·0.01·4
Δ = 1.2324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.18)-\sqrt{1.2324}}{2*0.01}=\frac{1.18-\sqrt{1.2324}}{0.02}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.18)+\sqrt{1.2324}}{2*0.01}=\frac{1.18+\sqrt{1.2324}}{0.02}
$